Using non-rigid-foldable origami patterns to design mechanical metamaterials could potentially offer more versatile behaviors than the rigid-foldable ones, but their applications are limited by the lack of analytical framework for predicting their behavior. Here, we propose a theoretical model to characterize a non-rigid-foldable square-twist origami pattern by its rigid origami counterpart. Based on the experimentally observed deformation mode of the square-twist, a virtual crease was added in the central square to turn the non-rigid-foldable pattern to a rigid-foldable one. Two possible deformation paths of the non-rigid-foldable pattern were calculated through kinematic analysis of its rigid origami counterpart, and the associated energy and force were derived analytically. Using the theoretical model, we for the first time discovered that the non-rigid-foldable structure bifurcated to follow a low-energy deformation path, which was validated through experiments. Furthermore, the mechanical properties of the structure could be programmed by the geometrical parameters of the pattern and material stiffness of the creases and facets. This work thus paves the way for development of non-rigid-foldable origami-based metamaterials serving for mechanical, thermal, and other engineering applications.